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i

NASA/TP—2014–218193

On the Relationship Between Global 

Land-Ocean Temperature and Various 

Descriptors of Solar-Geomagnetic 

Activity and Climate

Robert M. Wilson

Marshall Space Flight Center, Huntsville, Alabama

April 2014

National Aeronautics and

Space Administration

Marshall Space Flight Center • Huntsville, Alabama 35812
ii

Available from:

NASA STI Information Desk

Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681–2199, USA

757–864–9658

This report is also available in electronic form at

<http://www.sti.nasa.gov>
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

2. RESULTS ........................................................................................................................... 2

3. DISCUSSION AND SUMMARY ..................................................................................... 35

REFERENCES........................................................................................................................ 38
iv

LIST OF FIGURES

 1. Annual variation of (a) GLOTI, (b) SSN, (c) SSA, and (d) G ................................ 3

 2. Annual variation of ratios (a) SSN/G, (b) SSA/SSN, and (c) SSA/G ..................... 6

 3. Annual variation of (a) the aa index, (b) aa(SSN), and (c) aa(G) .......................... 8

 4. Scatter plots of (a) aa versus SSN and (b) aa versus G .......................................... 9

 5. Annual variation of (a) aa(I:SSN) and (b) aa(I:G) ................................................ 10

 6. Annual variation of asymmetries (a) [aa(I:SSN) –aa(SSN)]/aa 

and (b) [aa(I:G) – aa(G)]/aa .................................................................................... 11

 7. Variation of SC averages of <GLOTI> for lag 0–5 yr ........................................... 13

 8. Variation of SC averages of (a) <SSN>, (b) <SSA>, (c) <G>, (d) <aa>, 

(e) <aa(SSN)>, (f) <aa(I:SSN)>, (g) <aa(G)>, and (h) <aa(I:G)> ........................ 14

 9a. Scatter plots of <GLOTI> versus <SSN> for lag 0–5 yr ....................................... 15

 9b. Scatter plots of <GLOTI> versus <aa> for lag 0–5 yr ........................................... 16

 10a. Scatter plots of <GLOTI> versus <aa(I:SSN)> for lag 0–5 yr .............................. 17

 10b. Scatter plots of <GLOTI> versus <aa(I:G)> for lag 0–5 yr ................................... 18

 11. Annual variation of (a) AMO, (b) SOI, (c) NAO, (d) PDO, and (e) MLCO2 ........ 23

 12. Variation of SC averages of (a) <AMO>, (b) <SOI>, (c) <NAO>, 

(d) <PDO>, and (e) <MLCO2> ............................................................................ 25

 13a. Scatter plots of <GLOTI> versus <AMO> for lag 0–5 yr ..................................... 27

 13b. Scatter plots of <GLOTI> versus <SOI> for lag 0–5 yr ........................................ 28

 13c. Scatter plots of <GLOTI> versus <NAO> for lag 0–5 yr ...................................... 29

 13d. Scatter plots of <GLOTI> versus <PDO> for lag 0–5 yr ...................................... 30
v

LIST OF FIGURES (Continued)

 13e. Scatter plots of <GLOTI> versus <MLCO2> for lag 0–5 yr ................................. 31

 14. Annual variation of GLOTI for SC23 (filled circles) and SC24 (filled triangles) 

for similar phasing ................................................................................................. 33

 15. Annual variation of (a) GLOTI, (b) aa(SSN) and aa(I:SSN), (c) the AGGI, 

and (d) the radiative forcing of NO2, CH4, CO2, and total (including CFC12, 

CFC11, and 15 minor contributors) for the interval 1979–2012 ............................. 37
vi

LIST OF TABLES

 1a. Sunspot cycle epochs and selected parametric values—epochs and values ................ 12

 1b. Sunspot cycle epochs and selected parametric values—SC-length GLOTI 

values for lag=0–5 yr ................................................................................................ 12

 2. Correlations of SC averages of GLOTI against SC averages of selected 

parameters of solar-geomagnetic activity, incorporating lag 0–5 yr ........................... 20

 3. SC-length climate parametric mean values ................................................................ 25

 4. Correlations of SC-length averages of GLOTI against SC averages of selected 

climate parameters .................................................................................................... 32
vii

LIST OF ABBREVIATIONS, ACRONYMS, DESIGNATORS, AND SYMBOLS

aa aa-geomagnetic (index)

<aa> SC-length averaged aa

aa(G) portion of aa index due to G

<aa(G)> SC-length averaged aa(G)

aa(I:G) portion of the aa index remaining following removal of aa(G)

<aa(I:G)> SC-length averaged aa(I:G)

aa(I:SSN) portion of the aa index remaining following removal of aa(SSN)

<aa(I:SSN)> SC-length averaged aa(I:SSN)

aamin minimum amplitude of the aa index

aa(SSN) portion of aa index due to SSN

<aa(SSN)> SC-length averaged aa(SSN)

AGGI annual greenhouse gases index

AMO Atlantic Multidecadal Oscillation (index)

<AMO> SC-length averaged AMO

CFC11 chlorofluorocarbon 11

CFC12 chlorofluorocarbon 12

CH4 methane

CO2 carbon dioxide

Emax epoch of maximum amplitude

Emin epoch of minimum amplitude
viii

LIST OF ABBREVIATIONS, ACRONYMS, DESIGNATORS, AND SYMBOLS (Continued)

ENSO El Niño Southern Oscillation

G number of sunspot groups

<G> SC-length averaged G

GLOTI Global Land-Ocean Temperature Index

<GLOTI> SC-length averaged GLOTI

MLCO2 Mauna Loa CO2 (index)

<MLCO2> SC-length averaged MLCO2

N number of individual spots

NAO North Atlantic Oscillation (index)

<NAO> SC-length averaged NAO

NO2 nitrous oxide

ONI Oceanic Niño Index

PDO Pacific Decadal Oscillation (index)

<PDO> SC-length averaged PDO

Rmax maximum sunspot amplitude

SC sunspot cycle

SOI Southern Oscillation Index

<SOI> SC-length averaged SOI

SSA sunspot area

<SSA> SC-length averaged SSA

SSN sunspot number
ix

LIST OF ABBREVIATIONS, ACRONYMS, DESIGNATORS, AND SYMBOLS (Continued)

<SSN> SC-length averaged SSN

SST sea surface temperature

THC thermohaline circulation

TP Technical Publication
x

NOMENCLATURE

a y-intercept

b slope

cl confidence level

k reduction coefficient

n number

r coefficient of linear correlation

r2 coefficient of determination

sd standard deviation

se standard error of estimate

t t-statistic; elapsed time from Emin

x independent variable

y dependent variable
1

TECHNICAL PUBLICATION

ON THE RELATIONSHIP BETWEEN GLOBAL LAND-OCEAN TEMPERATURE 

AND VARIOUS DESCRIPTORS OF SOLAR-GEOMAGNETIC 

ACTIVITY AND CLIMATE

1. INTRODUCTION

It has long been recognized that a close association must exist between variations on the Sun 

and variations in Earth’s climate.1–59 As previously noted by Gray et al.60 in modern times, it was 

Sir William Herschel61 who first speculated (in 1801) that the Sun’s variations might directly influence Earth’s climate. More recently, Stauning62 (in 2011) reported that a strong statistical linear correlation appears to exist between averages of solar activity (i.e., sunspot number (SSN)) and global 

terrestrial temperature anomalies (at least up until 1985) when they are averaged over the same interval lengths (i.e., the sunspot cycle (SC)) but with the global temperature anomaly averages delayed by 

three years. Examined in this Technical Publication (TP) are determinations of the relative strengths 

of the inferred statistical correlations (incorporating lag=0–5 yr) between SC-length averages of the 

Global Land-Ocean Temperature Index (GLOTI) and SC-length averages of various descriptors of 

solar-geomagnetic activity and climate, including: (1) SSN, (2) sunspot area (SSA), (3) the number of 

sunspot groups (G), (4) the aa-geomagnetic (aa) index, (5) aa(SSN) (i.e., that portion of the aa index 

attributable directly to yearly variations in SSN), (6) the aa(I:SSN) (i.e., that portion of the aa index 

not attributable to yearly variations in SSN), (7) aa(G) (i.e., that portion of the aa index attributable 

directly to yearly variations in G), (8) aa(I:G) (i.e., that portion of the aa index not attributable to 

yearly variations in G), (9) the Atlantic Multidecadal Oscillation (AMO) index, (10) the Southern 

Oscillation Index (SOI), (11) the North Atlantic Oscillation (NAO) index, (12) the Pacific Decadal 

Oscillation (PDO) index, and (13) the Mauna Loa carbon dioxide (CO2) (MLCO2) index. Based 

on the best inferred preferential linear correlation, an estimate is also given for the expected average 

GLOTI for SC24 (and for SC25), where SC24 is the current ongoing SC, which had a cycle minimum 

annual amplitude based on SSN, SSA, and G in 2008.
2

2. RESULTS

Figure 1 displays the variation of the annual January–December averages of (a) GLOTI 

for the yearly interval 1880–2012, and (b) SSN, (c) SSA, and (d) G, where the variations of SSN, 

SSA, and G span the interval 1875–2012. For GLOTI, it appears to have been trending downwards (cooling) between 1880 and about 1910, but rising (warming) thereafter with a somewhat 

flattening occurring between about 1935 and 1975. The lowest (coolest) annual value of the GLOTI 

(to date) measures –0.46 °C in 1909, and the highest (warmest) annual value (to date) measures 

0.66  °C in 2010. For the interval 1880–2012, the GLOTI averages 0.013 °C and has a standard 

deviation sd=0.289 °C. For the interval 1976–2012, which corresponds to SC21 through the rising 

portion of ongoing SC24, linear regression analysis suggests that the GLOTI is related to year by 

the expression y=–33.227+0.017x, having a coefficient of linear correlation r=0.896, a coefficient 

of determination r2=0.803 (meaning that about 80% of the variance in the GLOTI for the interval 

1976–2012 can be explained by the inferred regression), a standard error of estimate se=0.109 °C, 

and a confidence level for the regression cl>99.9%. Extrapolation of the inferred regression beyond 

2012 suggests that the GLOTI possibly will continue to rise with the passage of time at the rate of 

about 0.017 °C per year, inferring that the GLOTI is expected to measure about 0.80±0.11 °C in 

the year 2020 (the ±1 se prediction interval), unless of course another flattening occurs or another 

downward trend develops. The annual values of the GLOTI represent deviations (anomalies) from 

the mean using the base period 1951–1980. (The values of the GLOTI used in this TP were taken 

from <http://data.giss.nasa.gov/gistemp/tabledata_v3/GLB.Ts+dSST.txt> in October 2013.)
3

GLOTI (°C)

G SSA SSN

Global Land-Ocean Temperature Index

1880–2012

1

0.5

0

–0.5

200

150

100

50

0

0

12 13 14 15 16 17 18 19 20 21 22 23 24

1,000

2,000

3,000

4,000

5

0

10

15

20

Most Reliable SSN

3,048.5 (1957)

14.90 (1979)

Groups

1875–2012

Sunspot Area

1875–2012

Sunspot Number

1875–2012

mean = 0.013 °C

sd = 0.289 °C

mean = 54.8

sd = 45.1

mean = 4.73

sd = 3.70

mean = 838.7 (× 10–6 Solar Hemisphere)

sd = 747.7 (× 10–6 Solar Hemisphere)

1920 1940 1960 1980 2000 2020

Year

1880 1900

(d)

(c)

(b)

(a)

190.2 (1957)

–0.46 (1909)

y 1976–2012 (r = 0.896, se = 0.109 °C)

0.66 °C (2010)

Figure 1. Annual variation of (a) GLOTI, (b) SSN, (c) SSA, and (d) G.
4

For SSN, its annual variation describes the episodic nature of sunspots, a variation directly 

attributable to the action of the SC. Plainly, SSN increases from a minimum value marking the onset 

of the SC (called cycle minimum amplitude and identified by the unfilled triangles) to a maximum 

value (called cycle maximum amplitude and identified by the filled triangles), which occurs about 

3–5 yr after cycle minimum amplitude, and then decreases over time to another minimum amplitude, 

marking the onset of the next SC. Samuel Heinrich Schwabe63 was the first to suggest the existence 

of the ‘sunspot cycle,’ a term used today to describe the overall variation of SSN over time, where 

each individual cycle has a minimum-to-minimum length (or period) of about 10–12 yr, with stronger 

cycles attaining cycle maximum amplitude more quickly than weaker cycles and often also being of 

shorter duration. In the span of SC12 to SC23, SC19 is the strongest cycle (to date), having the highest cycle maximum amplitude, measuring 190.2 in 1957, while SC14 is the weakest cycle (to date), 

having cycle maximum amplitude measuring only 63.5, a value slightly smaller than SC12’s cycle 

maximum amplitude of 63.7. For the yearly interval 1875–2012, SSN averages 54.8 and has sd=45.1. 

While the trend in SSN has been generally upwards between SC14 and SC19, it now appears to be 

trending downwards. The most reliable values of SSN are those found to span the yearly interval 

1882–2012, based on comparison of SSN against group SSN.64 Prior to 1981, the SSN was determined by the Swiss Federal Observatory based upon observations made at Zürich, Switzerland, 

and its two branch stations at Arosa and Locarno, and was known as the ‘Zürich relative sunspot 

number.’ Beginning in 1981 and continuing through today, the task of determining the SSN, now 

called the International Sunspot Number, was taken up by the Solar Influences Data Analysis Center, formerly known as the Sunspot Index Data Center, which is located at the Royal Observatory of 

Belgium <http://www.ngdc.noaa.gov/stp/solar/ssndata.html>. (The SSN values are available online 

at <http://sidc.oma.be/index.php3>.)

For SSA, its variation generally mimics that of SSN, although the occurrences of some of 

the extremes sometimes differ. For example, the cycle minimum amplitude for SC20 in terms of SSA 

is found to precede the cyclic minimum amplitude in terms of SSN by 1 yr, and the cycle maximum 

amplitude in terms of SSA for SC20, SC21, and SC23 is found to follow the cycle maximum amplitude in terms of SSN by 2, 3, and 2 yr, respectively. Also, about half of the cycles display a more 

double-peaked appearance in terms of SSA than in terms of SSN. The highest SSA (to date) measures 3,048.5 millionths of a solar hemisphere in 1957, associated with SC19. Interestingly, the cycle 

maximum amplitude in terms of SSA for SC12 is slightly smaller than that for SC14: 1,148.9 versus 

1,195.9 millionths of a solar hemisphere (in contrast to that found using SSN). For the interval 

1875–2012, the SSA averages 838.7 millionths of a solar hemisphere and has sd=747.7 millionths of 

a solar hemisphere. (Annual values of the SSA were taken from <http://solarscience.msfc.nasa.gov/

greenwch.shtml>.)

For G, it too generally mimics the behavior of SSN, although like SSA, the individual cycle’s 

maximum amplitude sometimes falls later than is seen in SSN. For example, the cycle maximum 

amplitude in terms of G for SC12 follows that of the cycle maximum amplitude in terms of SSN by 

1 yr. Also, the cycle maximum amplitudes in terms of G for SC14, SC19, and SC22 follow the cycle 

maximum amplitudes in terms of SSN by 2, 1, and 1 yr, respectively; however, the cycle maximum 

amplitude in terms of G for SC20 is found to precede the cycle maximum amplitude in terms of 

SSN by 1 yr (a later-occurring, slightly smaller secondary maximum amplitude in terms of G was 

observed simultaneously with the maximum amplitude in terms of SSA some 2 yr after the SSN 
5

maximum amplitude). About one-third of the cycles are found to display a double-peaked appearance. The highest G (to date) measures 14.90 in 1979, associated with SC21. For the interval 1875–

2012, G averages 4.73 and has sd=3.70. (G is determined directly from the SSA data set.)

Figure 2 depicts the ratios (a) SSN/G, (b) SSA/SSN, and (c) SSA/G for the yearly interval 

1875–2012, where the ratios are used to infer the variation of the ‘magnetic complexity’ of sunspots 

over individual SCs, with larger ratios, on average, suggesting greater magnetic complexity and smaller 

ratios suggesting lesser magnetic complexity for each individual SC. For SSN/G, although the maximum value is 19.68 in 1877, the year prior to the minimum amplitude for SC12, this value appears to 

be erroneous. Recall that the most reliable portion of the SSN record spans 1882 to 2012. A change 

occurred in the SSN record around 1882, when the k factor was reduced from 1 to 0.6 (Waldmeier65) 

in order to account for smaller spots that were being counted (the relative SSN is calculated based 

on the formulation SSN=k(10G+N), where k is a reduction coefficient, G is the number of groups, 

and N is the number of actual individual spots). Because the maximum value of the ratio SSN/G 

occurs near the minimum amplitude for SC12 (1878), because G is accurately determined from the 

Royal Greenwich Observatory photographic plate record, and because all SSN/G values during the 

early yearly interval 1875–1882 (except the value for 1881) are higher than all succeeding values 

during the interval 1882–2012 together, this suggests that the ratio values SSN/G during the early 

yearly interval 1875–1881 probably are in error, inferring that the SSN values during the early yearly 

interval 1875–1881 probably are too high. For the overall yearly interval 1875–2012, SSN/G averages 

11.38 and has sd=1.84. Ignoring the early ratios, the largest ratios (to date) measure 14.30 in 1957 

(SC19) and 14.28 in 1980 (SC21). Generally, the largest ratio occurs near SC maximum amplitude, 

and the smallest ratio occurs near SC minimum amplitude for individual cycles. The lowest observed 

ratio (to date) measures 7.50 in 1911 (late SC14 near cycle minimum amplitude for SC15). For the 

subyearly interval 1957–2012, one infers that SSN/G appears to be trending downwards, given by the 

expression y=80.572–0.035x, having r=–0.436, r2=0.19, se=1.186, and cl>99.9%, inferring that 

the maximum value of the ratio SSN/G for SC24 probably will be ≤11.56. Interestingly, the observed 

ratios during the rise of SC24 are smaller than were seen for similar phasing during SC14, suggesting perhaps that SC24 might turn out to be smaller in terms of SSN than that of SC14. (To date, the 

maximum ratio SSN/G during SC24 measures 11.43, occurring in 2012, having risen from 8.79 in 

2009. For an overview of the history of SSN indices, see <http://www.aavso.org/dances-wolfs-shorthistory-sunspot-indices>.)

For SSA/SSN, because values of SSN appear to be too high for the interval 1875–1882, the 

early values of SSA/SSN probably are too low. The largest ratio of SSA/SSN (to date) measures 19.77 

in 1926 (SC16), slightly larger than two other large ratios, both measuring 19.70 that occurred in 1946 

(SC18) and 1982 (SC21). The smallest ratio of SSA/SSN (to date) measures 5.28 in 1964 (SC20, cycle 

minimum). For the yearly interval 1875–2012, SSA/SSN averages 14.01 and has sd=3.20. Unlike 

SSN/G, there appears to be no preferential downward trend in SSA/SSN. For the current ongoing 

SC24, SSA/SSN has varied between 7.86 in 2008 and 13.86 in 2012, values that are lower than were 

seen in SC14, which varied between 10.33 and 18.83 for similar phasing (1901–1905).
6

SSA/G

50

0

100

150

200

250

300

Most Reliable SSN

44.1 (1913)

mean = 158.7 (× 10–6 Solar Hemisphere)

sd = 40.4 (× 10–6 Solar Hemisphere)

1920 1940 1960 1980 2000 2020

Year

1880 1900

(c)

230 (1883) 234.4 (1946)

y 1946–2012 (r = –0.278, se = 41.9)

SSA/SSN

5

0

10

15

20

mean = 14.01 (× 10–6 Solar Hemisphere)

sd = 3.20 (× 10–6 Solar Hemisphere)

(b)

5.28 (1964)

19.70 (1946) 19.70 (1982)

19.77

(1926)

SSN/G

5

0

10

15

20

mean = 11.38

sd = 1.84

(a)

7.50 (1911)

19.68 (1877) 

y 1957–2012 (r = –0.436, se = 1.186)

Figure 2. Annual variation of ratios (a) SSN/G, (b) SSA/SSN, and (c) SSA/G.
7

For SSA/G, the two largest ratios (to date) measure 230 in 1883 (SC12) and 234.4 in 1946 

(SC18). The smallest ratio (to date) measures 44.1 in 1913 (SC15, cycle minimum). For the yearly 

interval 1875–2012, SSA/G averages 158.7 and has sd=40.4. Like the ratio SSN/G, the ratio SSA/G 

appears to be trending downwards with the passage of time, given by the expression y=1,379.3 –0.617x, 

having r=–0.278, r2=0.08, se=41.9, and cl>95%. For the current ongoing SC24, SSA/G has varied 

between 69.1 in 2008 and 157.8 in 2012, values that are lower than were seen in SC14, which varied 

between 126.8 and 225.2 for similar phasing (1901–1905).

Figure 3 displays the annual values of (a) the aa index, (b) aa(SSN), and (c) aa(G) for the 

yearly interval 1875–2012. For the aa index, it has varied between 6.1 nT in 1901 (SC14) and 37.1 nT 

in 2003 (SC23), averaging 19.3 nT and having sd=6.3 nT for the overall yearly interval 1875–2012. 

The aa index correlates strongly with the solar wind speed and the occurrences of the southwardpointing interplanetary magnetic field at Earth.66–68 It should be noted that Svalgaard et al.69 have 

suggested that the observed aa index values before 1957 be increased by about 3 nT to compensate for movements of the magnetometers in Australia, which are used in the computation of the 

aa index. Doing so, one finds that the minimum amplitude of the aa index value (aamin) would now 

become 8.6 nT, which is the minimum amplitude value for SC24 in 2009. (The value of aamin usually 

follows SSN cycle minimum by one year and correlates strongly with the later-occurring SSN cycle 

maximum for each individual SC.)66,70–72

For aa(SSN) and aa(G), as previously noted, these parameters represent those portions of 

the aa index value directly attributable to the variation of the SC (dependent upon whether one uses 

SSN or G, respectively, to describe the SC). For aa(SSN), its peak value (to date) measures 26.2 nT 

in 1957 (SC19), and aa(SSN) is found to average 11.6 nT and have sd=4.8 nT for the yearly interval 

1875–2012, while for aa(G), its peak value (to date) measures 22.5 nT in 1979 (SC21), and aa(G) is 

found to average 11.1 nT and have sd=4.1 nT. (Notice that the minimum value for aa(G) is of comparable size for SC12, SC14, SC15, and SC24.)

Figure 4 displays scatter plots of aa versus (a) SSN and (b) G, where the diagonal lines represent aa(SSN) and aa(G), respectively, following the approach used by Feyman (ignoring the lone 

outlier associated with SSN for 1980, the point plotted below the aa(SSN) line).73,74 In the scatter 

plots, aa(SSN)=5.81+0.107SSN, and aa(G)=5.85+1.117G. As an example, SC19 had a maximum 

amplitude in terms of SSN (Rmax) equal to 190.2 in 1957, thus yielding aa(SSN)=26.2 nT.
8

aa(G)

30

25

20

15

10

5

0

22.5 nT (1979)

aa Portion Due to G

1875–2012

mean = 11.1 nT

sd = 4.1 nT

1920 1940 1960 1980 2000 2020

Year

1880 1900

(c) aa(SSN)

30

25

20

15

10

5

0

26.2 nT (1957)

aa Portion Due to SSN

1875–2012

mean = 11.6 nT

sd = 4.8 nT

(b)

6.1 nT (1901)

aa

30

35

40

25

20

15

10

5

37.1 nT (2003)

aa-Geomagnetic Index

1875–2012

mean = 19.3 nT

sd = 6.3 nT

(a)

Figure 3. Annual variation of (a) the aa index, (b) aa(SSN), and (c) aa(G).
9

aa

30

35

40

25

20

15

10

5

0

1875–2012

aa(G) = 5.85 + 1.117 G

aa(G)

0 5 10 15

G

0 50 100 150 200

SSN

(b) aa

30

35

40

25

20

15

10

5

1875–2012

aa(SSN) = 5.81 + 0.107SSN

aa(SSN)

(a)

Figure 4. Scatter plots of (a) aa versus SSN and (b) aa versus G.

Figure 5 shows the annual values of (a) aa(I:SSN) and (b) aa(I:G), those portions of the 

aa index not attributed to SSN or G, respectively. Recall that Feyman suggested that the aa index can 

be simply decomposed into two components: aa(SSN) and aa(I:SSN) (or aa(G) and aa(I:G)).73,74

The aa(SSN) (or aa(G)) component is that component due to the sporadic, short-lived events occurring on the Sun, which varies over the SC in phase with SSN (or G). The aa(I:SSN) (or aa(I:G)) 

component is that component due to the recurrent, long-lived events, like coronal holes (regions 

on the Sun that are the sources of the high-speed recurrent streams of solar wind, typically seen
10

aa Portion Not Due to SSN

aa(I:SSN) = aa–aa(SSN)

1875–2012

aa Portion Not Due to G

aa(I:G) = aa–aa(G)

1875–2012

aa(I:G)

30

25

20

15

10

5

0

mean = 8.2 nT

sd = 5.0 nT

1920 1940 1960 1980 2000 2020

Year

1880 1900

(b)aa(I:SSN)

30

25

20

15

10

5

0

24.5 nT (2003)

mean = 7.8 nT

sd = 5.1 nT

(a)

24.7 nT (2003)

Figure 5. Annual variation of (a) aa(I:SSN) and (b) aa(I:G).

during the declining portion of the SC between SSN cycle maximum amplitude and the succeeding 

cycle minimum amplitude marking the onset of the next SC) occurring on the Sun, which varies over 

the SC but is out of phase with respect to the phasing of aa(SSN) (or aa(G)). For aa(I:SSN), its peak 

value (to date) measures 24.5 nT in 2003, and for the yearly interval 1875–2012, aa(I:SSN) averages 

7.8 nT and has sd=5.1 nT. For aa(I:G), its peak value (to date) measures 24.7 nT in 2003, and for 

the yearly interval 1875–2012, aa(I:G) averages 8.2 nT and has sd=5.0 nT. (In the above example for 

SC19, the maximum amplitude of aa(I:SSN) is found to be 15 nT in 1960.) 

Figure 6 displays the variation of the asymmetry in the aa index for (a) [aa(I:SSN) – aa(SSN)]/

aa and (b) [aa(I:G)– aa(G)]/aa for the yearly interval 1875–2012. When the values are negative, this 

simply means that the sporadic component contributes more to the value of the aa index than the 

recurrent component, the opposite being true for positive values. For [aa(I:SSN)–aa(SSN)]/aa, it 

averages –0.24 and has sd=0.37. For [aa(I:G)–aa(G)]/aa, it averages –0.20 and has sd=0.35. Thus,
11

[aa(I:G)–aa(G)]/aa [aa(I:SSN)–aa(SSN)]/aa

1

1

0.5

0

0

–0.5

–1

0.5

–0.5

–1

mean = –0.20

sd = 0.35

1920 1940 1960 1980 2000 2020

Year

(b) 1880 1900

mean = –0.24

sd = 0.37

(a)

Figure 6. Annual variation of asymmetries (a) [aa(I:SSN) –aa(SSN)]/aa 

and (b) [aa(I:G) –aa(G)]/aa.

on average, the sporadic component has been the stronger contributor to the value of the aa index 

than the recurrent component. Close inspection reveals that this was especially true during SC14 

(1901–1912).

Table 1a identifies the epochs of the cycle minimum (Emin) and maximum (Emax), the 

minimum-to-minimum SC-length, the Rmax, the aamin, and SC averages of SSN, SSA, G, aa, 

aa(SSN), aa(I:SSN), aa(G), and aa(I:G) for each SC12–SC23. Also, table 1b identifies SC averages 

for the GLOTI, incorporating lags of 0–5 yr, relative to Emin.
12

Table 1a. Sunspot cycle epochs and selected parametric values—epochs and values.

Cycle Emin Emax Length Rmax aamin <SSN> <SSA> <G> <aa> <aa(SSN)> <aa(I:SSN)> <aa(G)> <aa(I:G)>

12 1878 1883 11 63.7 7.1 34.6 526.4 2.70 14.8 9.5 5.1 8.9 6.1

13 1889 1893 12 85.1 10.7 38.8 607.2 3.54 15.7 10.0 5.7 9.8 5.9

14 1901 1905 12 63.5 6.1 31.1 477.8 2.84 13.1 9.1 3.9 9.0 4.0

15 1913 1917 10 103.9 8.7 44.2 657.3 4.44 17.1 10.5 6.7 10.8 6.3

16 1923 1928 10 77.8 10.2 41.0 706.9 4.00 17.2 10.2 7.0 10.3 6.9

17 1933 1937 11 114.4 13.4 55.0 914.2 4.64 20.3 11.7 8.6 11.3 9.0

18 1944 1944 10 151.6 16.4 75.7 1,203.4 6.02 23.2 13.9 9.3 12.6 10.6

19 1954 1957 10 190.2 17.2 95.0 1,492.0 7.18 24.6 16.0 8.6 13.9 10.7

20 1964 1968 12 105.9 14.0 58.8 819.2 5.09 21.1 12.1 9.0 11.5 9.5

21 1976 1979 10 155.4 20.3* 82.9 1,273.0 7.39 24.9 13.8 11.8 14.1 10.8

22 1986 1989 10 157.6 19.0 78.5 1,141.7 6.82 25.9 14.2 11.6 13.5 12.4

23 1996 2000 12 119.6 16.1 56.6 839.0 4.92 21.9 11.9 10.1 11.4 10.6

24 2008 2012? – 57.5? 8.7 – – – – – – – –

Note: * SC21 had an aamin in the vicinity of Emin; however, its observed aamin was 18.3 occurring near Emax.

Table 1b. Sunspot cycle epochs and selected parametric values—SC-length 

GLOTI values for lag=0–5 yr.

Lag (yr)

Cycle 0 1 2 3 4 5

12 – – –0.217 –0.222 –0.238 –0.256

13 –0.246 –0.241 –0.253 –0.260 –0.271 –0.265

14 –0.373 –0.388 –0.382 –0.365 –0.358 –0.371

15 –0.295 –0.282 –0.283 –0.289 –0.262 –0.236

16 –0.174 –0.173 –0.158 –0.151 –0.152 –0.131

17 –0.022 0.014 0.023 0.029 0.023 0.023

18 –0.032 –0.057 –0.070 –0.080 –0.072 –0.059

19 –0.018 –0.027 –0.025 –0.011 –0.016 –0.025

20 –0.023 –0.016 0.005 0.013 0.024 0.048

21 0.128 0.155 0.169 0.198 0.210 0.226

22 0.291 0.309 0.325 0.351 0.367 0.368

23 0.526 0.539 0.551 0.555 0.568 0.583

Figure 7 plots the SC averages of the GLOTI (taken from table 1b). For all lags (0–5 yr), it is 

quite apparent that SC averages of GLOTI track upwards with the passage of time, with a noticeable 

flattening spanning SC17–SC20. Since SC20 (1964–1975), the GLOTI values have consistently risen 

with the passage of time, with the current ongoing rise in the SC average value of the GLOTI being 

of steeper slope than the previous one found for the preceding interval SC14–SC17.
13

<GLOTI>

–0.5

0

0.5

1 Lag = 0 Lag = 1

Lag = 3

12 14

Lag = 5

16 18 20 22 24

SC

<GLOTI>

–0.5

0

0.5

1 Lag = 2

<GLOTI>

–0.5

0

0.5

1

12 14

Lag = 4

16 18 20 22 24

SC

Figure 7. Variation of SC averages of <GLOTI> for lag 0–5 yr.
14

Figure 8 plots the SC averages of the eight solar-geomagnetic parameters (taken from 

table 1a). Some similarity is noticeable between these parameters and <GLOTI>, in particular with 

<aa(I:SSN)> and <aa(I:G)>. <SSN> 50

0

100

<SSA> 1,000

2,000

<G>

5

0 0

10

<aa> 20

10

30

<aa(I:SSN)> 8

16

<aa(G)> 8

0

16

<aa(SSN)> 8

0 0

16<aa(I:G)> 8

0

16

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

SC

12 14 16 18 20 22 24

(a) (b)

(d)

(c)

(f)

(g) (h)

(e)

Figure 8. Variation of SC averages of (a) <SSN>, (b) <SSA>, (c) <G>, (d) <aa>,

(e) <aa(SSN)>, (f) <aa(I:SSN)>, (g) <aa(G)>, and (h) <aa(I:G)>.
15

Figure 9a displays the scatter plots of <GLOTI> versus <SSN>, and figure 9b displays 

scatter plots of <GLOTI> versus <aa> for lags of 0–5 yr for the groupings SC12–SC21 and SC12–

SC23. It is apparent that SC23 (and possibly SC22, both plotted as filled squares) is a statistical outlier with respect to the inferred regression based on SC12–SC21. In contrast to that of Stauning,62

the strongest inferred linear correlation between <GLOTI> and <SSN> using SC12–SC21 is the one 

incorporating lag=0 yr, having r=0.83 and se=0.09 °C. (This is also true for <GLOTI> versus <aa> 

for lag=0 yr, having r=0.93 and se=0.07 °C.) <GLOTI> (lag 0)

0.6

–0.6

0

23

22

17 20

16

15 13

14

18 19

21

y13–23 (r =0.54)

y13–21 (r =0.83)

<GLOTI> (lag 1)

0.6

–0.6

0

23

22

17

20

16

15 13

14

18 19

21

y13–23 (r =0.53)

y13–21 (r =0.79)

<GLOTI> (lag 3)

0.6

–0.6

0

23

22

17 20

16

15 13

12

14

18 19

21

y12–23 (r =0.57)

y12–21 (r =0.78)

<GLOTI> (lag 2)

0.6

–0.6

0

23

22

17 20

16

15 13

12

14

18 19

21 y12–23 (r =0.56)

y12–21 (r =0.78)

<GLOTI> (lag 5)

0.6

–0.6

0

<SSN>

0 50

23

22

17

20

16

15

13 12

14

18 19

21

100

y12–23 (r =0.56)

y12–21 (r =0.77)

<GLOTI> (lag 4)

0.6

–0.6

0

<SSN>

<SSN> <SSN>

<SSN> <SSN>

0 50

23

22

17 20

16

15 13

12

14

18 19

21

100

0 50 100 0 50 100

0 50 100 0 50 100

y12–23 (r =0.57)

y12–21 (r =0.79)

Figure 9a. Scatter plots of <GLOTI> versus <SSN> for lag 0–5 yr.
16 <GLOTI> (lag 0)

0.6

–0.6

0

<GLOTI> (lag 1)

0.6

–0.6

0

0 20

23

22

17

16 20

15

13

14

18 19

21

30

y13–23 (r =0.75)

y13–21 (r =0.93)

0 20

23

22

17

16 20

15

13

14

18 19

21

30

y13–23 (r =0.74)

y13–21 (r =0.91)

<GLOTI> (lag 2)

0.6

–0.6

0

<GLOTI> (lag 3)

0.6

–0.6

0

0 20

23

22

17 20

16

15 13

12

14

18 19

21

30

y12–23 (r =0.75)

y12–21 (r =0.89)

0 20

23

22

17 20

16

15 13

14

12 18 19

21

30

y12–23 (r =0.76)

y12–21 (r =0.88)

<GLOTI> (lag 4)

0.6

–0.6

0

<GLOTI> (lag 5)

0.6

–0.6

0

<aa>

0 20

23

22

17 20

16

13 15

12

14

18 19

21

30

y12–23 (r =0.76)

y12–21 (r =0.89)

<aa>

<aa> <aa>

<aa> <aa>

0 20

23

22

17 20

16

15 13

14

12 18 19

21

30

y12–23 (r =0.76)

y12–21 (r =0.89)

Figure 9b. Scatter plots of <GLOTI> versus <aa> for lag 0–5 yr.

Figure 10a shows the scatter plots of <GLOTI> versus <aa(I:SSN)>, and figure 10b shows the 

scatter plots of <GLOTI> versus <aa(I:G)> for lags of 0–5 yr. All inferred correlations are stronger 

than those based on either <SSN> or <aa> (shown in figs. 9a and 9b). The strongest inferred linear 

correlation using the grouping SC12–SC21 appears to be that of <GLOTI> versus <aa(I:SSN)> for 

lag=5 yr, having r=0.97 and se=0.05 °C. (For <GLOTI> versus <aa(I:G)>, the strongest inferred 

correlation using the grouping SC12–SC21 appears to be the one incorporating lag=0 yr, having 

r=0.95 and se=0.05 °C.)
17

<GLOTI> (lag 0)

0.6

–0.6

0

23

22

17, 19

20 16

15

13

14

18

21

y13–21 (r =0.96)

y13–23 (r =0.88)

<GLOTI> (lag 1)

0.6

–0.6

0

23

22

17 19

16

15

13

14

18

21

y13–21 (r =0.96)

y13–23 (r =0.84)

<GLOTI> (lag 2)

0.6

–0.6

0

25

22

17

20

16

15

13 12

14

18

19

21

y12–21 (r =0.94)

y12–23 (r =0.84)

<GLOTI> (lag 3)

0.6

–0.6

0

23

22

19

17

16

15 13

12

14

18

20

21

y12–21 (r =0.94)

y12–23 (r =0.85)

<GLOTI> (lag 4)

0.6

–0.6

0

23

22

17

16

13 15

12

14

18

21

y12–21 (r =0.96)

y12–23 (r =0.86)

<GLOTI> (lag 5)

0.6

–0.6

0

23

22

19

17

16

15 13

12

14

18

20 21

y12–21 (r =0.97)

y12–23 (r =0.87)

0 6 12 0

<aa (I:SSN)> <aa (I:SSN)>

<aa (I:SSN)> <aa (I:SSN)>

<aa (I:SSN)> <aa (I:SSN)>

6 12

0 6 12 0 6 12

0 6 12 0 6 12

20

20 19

Figure 10a. Scatter plots of <GLOTI> versus <aa(I:SSN)> for lag 0–5 yr.
18

<GLOTI> (lag 0)<GLOTI> (lag 1)

0.6

–0.6

0

23

22

17

20 16

15

13

14

18

19

21

y13–23 (r =0.83)

y13–21 (r =0.95)

23

22

17

16 20

15

13

14

18

19

21

y13–23 (r =0.82)

y13–21 (r =0.92)

<GLOTI> (lag 2)<GLOTI> (lag 3)

0.6

–0.6

0

23

22

17

20 16

15

1312

14

18

19

21 y12–23 (r =0.83)

y12–21 (r =0.91)

23

22

17

20 16

15

1312

14

18

19

21 y12–23 (r =0.83)

y12–21 (r =0.90)

<GLOTI> (lag 4)<GLOTI> (lag 5)

0.6

–0.6

0 6 12

0

0.6

–0.6

0

0.6

–0.6

0

0.6

0

<aa(I:G)>

0 6 12

<aa(I:G)>

<aa(I:G)> <aa(I:G)>

<aa(I:G)> <aa(I:G)>

0 6 12 0 6 12

0 6 12 0 6 12

23

22

17

20 16

15

1312

14

18

19

21 y12–23 (r =0.83)

y12–21 (r =0.90)

23

22

17

20

16

15 13

14 12

18

19

21

y12–23 (r =0.83)

y12–21 (r =0.90)

Figure 10b. Scatter plots of <GLOTI> versus <aa(I:G)> for lag 0–5 yr.
19

Table 2 provides the statistics for each of the correlations of <GLOTI> versus the eight solargeomagnetic parameters, arranged according to r2, the coefficient of determination, for both groupings SC12–SC21 and SC12–SC23 and for lags 0–5 yr. For every case, the strongest inferred linear 

correlation is the one based on <aa(I:SSN)>. In table 2, the statistic a is the y-intercept, b is the slope,

r is the coefficient of linear correlation, r2 is the coefficient of determination, se is the standard error 

of estimate, t is the t-statistic for determining the statistical importance of the inferred linear correlation, n is the number of SC used in the analysis, and cl is the confidence level of the inferred linear 

correlation (based on n and t).
20Table 2. Correlations of SC averages of GLOTI against SC averages of selected parameters 

of solar-geomagnetic activity, incorporating lag 0–5 yr.

Lag 0, SC13–SC21 Lag 0, SC13–SC23

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t n cl

<aa(I:SSN)> –0.651 0.068 0.962 0.926 0.047 9.449 9 >99.9% <aa(I:SSN)> –0.783 0.091 0.834 0.695 0.153 4.544 11 >99.8%

<aa(I:G)> –0.627 0.062 0.950 0.902 0.053 8.262 9 >99.9% <aa(I:G)> –0.750 0.083 0.827 0.684 0.156 4.422 11 >99.8%

<aa> –0.838 0.037 0.934 0.873 0.069 6.327 9 >99.9% <aa> –0.980 0.047 0.746 0.556 0.185 3.370 11 >99.5%

<aa(G)> –1.042 0.081 0.872 0.761 0.089 4.550 9 >99.5% <aa(G)> –1.078 0.091 0.583 0.339 0.225 2.159 11 >90%

<G> –0.564 0.089 0.860 0.740 0.089 4.465 9 >99.5% <G> –0.538 0.100 0.573 0.328 0.227 2.099 11 >90%

<SSN> –0.474 0.006 0.831 0.691 0.093 4.038 9 >99.5% <SSN> –0.434 0.007 0.542 0.293 0.233 1.966 11 >90%

<SSA> –0.470 0.0004 0.824 0.679 0.103 3.784 9 >99% <aa(SSN)> –0.834 0.067 0.543 0.295 0.233 1.942 11 >90%

<aa(SSN)> –0.804 0.058 0.799 0.638 0.107 3.449 9 >98% <SSA> –0.394 0.0004 0.488 0.238 0.242 1.656 11 <90%

Lag 1, SC13–SC21 Lag 1, SC13–SC23

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t n cl

<aa(I:SSN)> –0.671 0.071 0.962 0.925 0.049 9.523 9 >99.9% <aa(I:SSN)> –0.804 0.094 0.841 0.707 0.154 4.652 11 >99.8%

<aa(I:G)> –0.631 0.063 0.923 0.852 0.069 6.445 9 >99.9% <aa(I:G)> –0.758 0.085 0.821 0.674 0.162 4.359 11 >99.8%

<aa> –0.845 0.037 0.908 0.824 0.074 5.894 9 >99.9% <aa> –0.993 0.048 0.741 0.549 0.191 3.326 11 >99%

<aa(G)> –1.053 0.082 0.848 0.718 0.097 4.203 9 >99.5% <aa(G)> –1.094 0.093 0.580 0.336 0.232 2.143 11 >90%

<G> –0.566 0.090 0.833 0.694 0.100 4.009 9 >99% <G> –0.541 0.102 0.568 0.323 0.234 2.076 11 >90%

<SSN> –0.468 0.006 0.791 0.626 0.109 3.443 9 >99% <SSN> –0.429 0.007 0.530 0.280 0.241 1.896 11 >90%

<SSA> –0.464 0.0004 0.785 0.616 0.117 3.327 9 >98% <aa(SSN)> –0.827 0.067 0.528 0.279 0.242 1.870 11 >90%

<aa(SSN)> –0.791 0.057 0.754 0.568 0.120 3.028 9 >98% <SSA> –0.388 0.0004 0.476 0.226 0.251 1.600 11 <90%

Lag 2, SC12–SC21 Lag 2, SC13–SC23

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t n cl

<aa(I:SSN)> –0.634 0.068 0.945 0.893 0.058 8.186 10 >99.9% <aa(I:SSN)> –0.766 0.091 0.843 0.711 0.152 4.946 12 >99.9%

<aa(I:G)> –0.622 0.063 0.911 0.830 0.073 6.257 10 >99.9% <aa(I:G)> –0.755 0.085 0.827 0.685 0.159 4.657 12 >99.9%

<aa> –0.800 0.035 0.888 0.788 0.076 5.831 10 >99.9% <aa> –0.962 0.047 0.750 0.562 0.187 3.599 12 >99.5%

<aa(G)> –0.957 0.075 0.821 0.674 0.104 4.003 10 >99.5% <aa(G)> –1.057 0.090 0.602 0.363 0.225 2.380 12 >95%

<G> –0.513 0.082 0.808 0.653 0.104 3.897 10 >99.5% <G> –0.520 0.099 0.592 0.351 0.228 2.316 12 >95%

<SSN> –0.451 0.006 0.780 0.608 0.113 3.527 10 >99% <SSN> –0.844 0.069 0.554 0.307 0.235 2.112 12 >90%

<SSA> –0.444 0.0004 0.771 0.595 0.122 3.395 10 >99% <aa(SSN)> –0.437 0.007 0.556 0.309 0.235 2.073 12 >90%

<aa(SSN)> –0.765 0.055 0.744 0.553 0.118 3.176 10 >98% <SSA> –0.400 0.0004 0.505 0.255 0.245 1.753 12 <90%
21

Table 2. Correlations of SC averages of GLOTI against SC averages of selected parameters 

of solar-geomagnetic activity, incorporating lag 0–5 yr (Continued).

Lag 3, SC12–SC21 Lag 3, SC12–SC23

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t n cl

<aa(I:SSN)> –0.644 0.070 0.940 0.883 0.063 7.767 10 >99.9% <aa(I:SSN)> –0.780 0.094 0.849 0.722 0.111 6.973 12 >99.9%

<aa(I:G)> –0.627 0.064 0.898 0.806 0.080 5.823 10 >99.9% <aa(I:G)> –0.764 0.087 0.830 0.689 0.161 4.702 12 >99.9%

<aa> –0.814 0.036 0.882 0.777 0.082 5.557 10 >99.9% <aa> –0.983 0.048 0.757 0.573 0.192 3.579 12 >99%

<aa(G)> –0.984 0.078 0.833 0.678 0.108 4.020 10 >99.5% <aa(G)> –1.093 0.094 0.615 0.378 0.227 2.467 12 >95%

<G> –0.523 0.086 0.811 0.658 0.109 3.907 10 >99.5% <G> –0.534 0.104 0.605 0.366 0.229 2.417 12 >95%

<SSN> –0.457 0.006 0.780 0.608 0.113 3.523 10 >99% <SSN> –0.866 0.071 0.562 0.316 0.238 2.145 12 >90%

<SSA> –0.451 0.0004 0.770 0.593 0.121 3.424 10 >99% <aa(SSN)> –0.447 0.007 0.566 0.321 0.239 2.037 12 >90%

<aa(SSN)> –0.780 0.057 0.740 0.548 0.124 3.115 10 >98% <SSA> –0.408 0.0004 0.515 0.266 0.249 1.720 12 <90%

Lag 4, SC12–SC21 Lag 4, SC12–SC23

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t n cl

<aa(I:SSN)> –0.654 0.072 0.956 0.913 0.056 8.956 10 >99.9% <aa(I:SSN)> –0.793 0.096 0.856 0.733 0.151 5.258 12 >99.9%

<aa(I:G)> –0.630 0.065 0.901 0.812 0.081 5.886 10 >99.9% <aa(I:G)> –0.772 0.088 0.830 0.690 0.164 4.677 12 >99.9%

<aa> –0.824 0.037 0.891 0.794 0.083 5.639 10 >99.9% <aa> –0.998 0.049 0.760 0.578 0.190 3.684 12 >99.5%

<aa(G)> –1.004 0.080 0.840 0.705 0.104 4.281 10 >99.5% <aa(G)> –1.117 0.096 0.622 0.387 0.229 2.497 12 >95%

<G> –0.532 0.088 0.829 0.687 0.104 4.185 10 >99.5% <G> –0.543 0.106 0.613 0.376 0.231 2.440 12 >95%

<SSN> –0.459 0.006 0.786 0.618 0.111 3.592 10 >99% <SSN> –0.450 0.008 0.568 0.323 0.238 2.340 12 >95%

<SSA> –0.451 0.0004 0.772 0.596 0.121 3.443 10 >99% <aa(SSN)> –0.876 0.072 0.563 0.317 0.242 2.144 12 >90%

<aa(SSN)> –0.785 0.058 0.744 0.554 0.126 3.127 10 >98% <SSA> –0.409 0.0004 0.514 0.264 0.254 1.689 12 <90%

Lag 5, SC12–SC21 Lag 5, SC12–SC23

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t n cl

<aa(I:SSN)> –0.672 0.075 0.969 0.939 0.048 10.944 10 >99.9% <aa(I:SSN)> –0.805 0.098 0.865 0.748 0.149 5.433 12 >99.9%

<aa(I:G)> –0.638 0.067 0.898 0.806 0.085 5.753 10 >99.9% <aa(I:G)> –0.776 0.090 0.831 0.690 0.164 4.560 12 >99.9%

<aa> –0.839 0.038 0.890 0.792 0.085 5.653 10 >99.9% <aa> –1.007 0.050 0.762 0.581 0.192 3.729 12 >99.5%

<aa(G)> –1.026 0.082 0.840 0.705 0.104 4.393 10 >99.5% <aa(G)> –1.131 0.098 0.625 0.391 0.232 2.524 12 >95%

<G> –0.540 0.091 0.831 0.690 0.107 4.222 10 >99.5% <G> –0.548 0.109 0.617 0.381 0.233 2.490 12 >95%

<SSN> –0.458 0.006 0.773 0.597 0.116 3.414 10 >99% <SSN> –0.446 0.008 0.565 0.319 0.242 2.302 12 >95%

<SSA> –0.448 0.0004 0.757 0.573 0.127 3.282 10 >98% <aa(SSN)> –0.874 0.073 0.559 0.312 0.246 2.139 12 >90%

<aa(SSN)> –0.787 0.058 0.731 0.534 0.129 3.048 10 >98% <SSA> –0.404 0.0004 0.510 0.260 0.259 1.656 12 <90%
22

Figure 11 displays the yearly variation of (a) AMO (1875–2012), (b) SOI (1875–2012), 

(c) NAO (1875–2012), (d) PDO (1900–2012), and (e) MLCO2 (1959–2012). The AMO is a fluctuation in the detrended sea surface temperature (SST) in the North Atlantic Ocean north of the equator (lat. 0°–70° N.).75–79 The AMO has a cycle length of about 65–70 years, alternating between 

warm (positive) and cold (negative) phases believed to be associated with variations in the North 

Atlantic thermohaline circulation (THC), a density-driven global circulation pattern that involves 

the movement of warm equatorial surface waters to higher latitudes and the subsequent cooling 

and sinking of these waters into the deep ocean (also called the Atlantic Meridional Overturning 

Circulation; see <http://www.eoearth.org/view/article/150290>). The warm phase of the AMO 

appears to represent intervals of faster THC, while the cold phase appears to represent intervals of 

slower THC. The AMO index values are available online at <http://www.esrl.noaa.gov/psd/data/

correlation/amon.us.long.data>.

The SOI describes the atmospheric response to anomalous changes in surface air pressure 

between Tahiti, French Polynesia, and Darwin, Australia, which generally varies inversely with the 

Oceanic Niño Index (ONI), an index that describes anomalous changes in SST in the Niño 3.4 region 

of the Pacific Ocean (located ±5° either side of the equator and ±25° either side of long. 145° W.).80

Together, the variations in SOI and ONI often are used to describe the anomalous warming 

(El Niño) and cooling (La Niña) events associated with the El Niño Southern Oscillation (ENSO) 

pattern.81 During warm events of the ENSO, the ONI≥0.5 °C, and the SOI typically is ≤–8 for at 

least five consecutive months, while during cool events, the ONI≤ –0.5 °C and SOI ≥8 for at least five 

consecutive months. Values of SOI (based on means and standard deviations over the period 1933–

1992 inclusive) are available online at <http://www.bom.gov.au/climate/current/soihtml.shtml>.

The NAO describes the differences in surface air pressure between two widely separated locations, in particular Iceland and the subtropical Atlantic Ocean basin (e.g., the Azores, Portugal, or 

Gilbraltar).82–85 The large-scale air mass movements described by the NAO controls the strength 

and direction of the westerly winds and storm tracks across the North Atlantic Ocean. During the 

positive phase of the NAO, there is a stronger subtropical high-pressure center and a deeper-thanusual Icelandic low, while during the negative phase, the opposite is true. Values for the NAO index 

are available online at <http://www.esrl.noaa.gov.psd/gcos_wgsp/Timeseries/Data/nao.long.data> 

and <http://www.cru.uea.ac.uk~timo/datapages/naoi.html>.

The PDO is defined as the leading principal component of the monthly SST anomalies in the 

North Pacific Ocean northward of lat. 20° N. The PDO fluctuates between warm (positive) and cool 

(negative) phases.86–88 During the warm phase, the western Pacific Ocean surface waters become 

cool, and part of the eastern Pacific Ocean surface waters becomes warm, while during the cool 

phase, the opposite is true. Values of the PDO index are available online at <http://jisao.washington.

edu/pdo/PDO.latest>. 

The MLCO2 is a measure of the atmospheric concentration of CO2 as measured at the Mauna 

Loa Observatory on the Big Island of Hawaii.89–95 The observatory is located on the northern slope 

of the volcano Mauna Loa at an elevation of 3,400 m above sea level and 800 m below its summit. 

Annual means of MLCO2 (in units of ppm) are available online at <ftp://ftp.cmdl.noaa.gov/ccg/co2/

trends/co2_annmean_mlo.txt>. 
23

AMO

0

0.5

1880 1900 1920 1940 1960 1980 2000 2020

mean = –0.009 °C

sd = 0.187 °C

(a) –0.422 (1974)

Atlantic Multidecadal Oscillation Index

1875–2012

SOI

0

25

–25

–0.5

mean = 0.12

sd = 6.88

(b) –20.0 (1905)

20.8 (1917)

0.452 (1878)

Southern Oscillation Index

1875–2012

NAO

0

3

–3

mean = 0.07

sd = 0.51

(c)

1.23 (1990)

–2.19 (2010)

North Atlantic Oscillation Index

1875–2012

PDO

0

2

–2

mean = 0.01

sd = 0.77

(d)

1.99 (1941)

–1.95 (1955)

Pacific Decadal Oscillation Index

1900–2012

MLCO2

300

Year

350

400

mean = 349.03 ppm

sd = 23.48 ppm

(e)

393.82 ppm (2012)

315.97 ppm (1959)

Mauna Loa CO2 Index

1959–2012

Figure 11. Annual variation of (a) AMO, (b) SOI, (c) NAO, (d) PDO, and (e) MLCO2.
24

Regarding the AMO, the highest value (to date) measures 0.452 °C in 1878, and the lowest value (to date) measures –0.422 °C in 1974. Overall, the long-term mean is –0.009 °C, having 

sd=0.187 °C. Clearly, the AMO has been increasing in value (i.e., becoming more positive in value, 

indicating warming) since 1974, with all values since 1995 (except the value for 1996) being of positive value.

Regarding the SOI, the highest value (to date) measures 20.8 in 1917, and the lowest value 

(to date) measures –20 in 1905. Overall, the long-term mean is 0.12, having sd=6.88.

Regarding the NAO, the highest value (to date) measures 1.23 in 1990, and the lowest value 

(to date) measures –2.19 in 2010. Overall, the long-term mean is 0.07, having sd=0.51.

Regarding the PDO, the highest value (to date) measures 1.99 in 1941, and the lowest value 

(to date) measures –1.95 in 1955. Overall, the long-term mean is 0.01, having sd=0.77.

Regarding the MLCO2, its values have consistently risen year to year from 315.97 ppm in 

1959 to 393.82 ppm in 2012. The long-term mean measures 349.03 ppm, having sd=23.48 ppm. 

Close inspection of the annual MLCO2 values reveals that not only is the atmospheric concentration 

of CO2 increasing with the passage of time, but it is increasing at an accelerated rate (as placement 

of a straight edge along the curve clearly shows).

Table 3 gives the SC-length averages of each of the climatic parameters for SC12–SC23, and 

figure 12 displays them. For <AMO>, the warm phase is associated with SC12, SC16–SC18, and 

SC23, while the cool phase is associated with SC14, SC15, and SC20–SC22 (SC13 and SC16 appear 

to be cycles in transition). Since the warm phase is expected to persist at least three cycles in length, it 

is anticipated that SC24 and SC25 very likely will both be associated with the warm (positive) phase 

of the AMO as well. Interestingly, both the lows and highs of each individual phase appear to be 

increasing in value with the passage of time; i.e., SC23 (the current warm phase) is of higher positive 

value than SC18 (during the previous warm phase), which was higher than the value for SC12 (during the earliest warm phase). Similarly, the low of SC20 (during the just past cool phase) is higher 

than the low of SC15 (during the previous cool phase).

Regarding <SOI>, it appears that SC19 and SC20 were both associated with positive SOI, 

inferring cooler waters in the Niño 3.4 region (i.e., the likely occurrence of more La Niña-like conditions, on average), while SC21 and SC22 were both associated with negative SOI, inferring warmer 

waters in the Niño 3.4 region (i.e., the likely occurrence of more El Niño-like conditions, on average). 

SC20 is associated with the highest <SOI> (to date), while SC22 is associated with the lowest <SOI> 

(to date).

Regarding <NAO>, it has tended to be mostly of positive value. The highest positive value 

(to date) of <NAO> is associated with SC22, while the lowest value (to date) of <NAO> is associated with SC23. It is unclear whether SC24 will be of positive or negative <NAO> value.
25

Table 3. SC-length climate parametric mean values.

Cycle <AMO> <SOI> <NAO> <PDO> <MLCO2>

12 0.087 0.58 0.03 – –

13 0.013 –0.49 0.25 – –

14 –0.168 0.24 0.23 – –

15 –0.225 1.48 0.22 –0.06 –

16 –0.012 1.06 0.11 0.33 –

17 0.126 –0.43 –0.004 0.72 –

18 0.137 0.16 0.22 –0.61 –

19 0.094 2.63 0.09 –0.58 –

20 –0.184 2.73 –0.05 –0.64 325.10

21 –0.170 –3.43 0.05 0.54 339.19

22 –0.091 –4.60 0.30 0.55 354.42

23 0.164 –0.73 –0.21 0.17 372.82

0.3

0

(a) –0.3 <AMO>

5

0

(b) –5 <SOI>

12 14 16 18 20 22 24

SC

Figure 12. Variation of SC averages of (a) <AMO>, (b) <SOI>,

(c) <NAO>, (d) <PDO>, and (e) <MLCO2>.
26

400

350

300

12 14 16 18 20 22 24

SC

(e)

1

0

(d) –1 <PDO>

0.3

0

(c) –0.3 <NAO> <MLCO2>

Figure 12. Variation of SC averages of (a) <AMO>, (b) SOI, (c) <NAO>, 

(d) <PDO>, and (e) <MLCO2> (Continued).

Regarding <PDO>, its highest positive value (to date) occurs in SC17, and its lowest negative 

value (to date) occurs in SC20. In appearance, its behavior looks similar to that of <AMO>, but of 

slightly different phase. Whereas the SC variation in <AMO> tends to have a smoother appearance, 

the SC variation in <PDO> is less smooth.

Regarding <MLCO2>, every cycle has a value that is higher than its preceding cyclic value. 

Hence, SC21 has a higher <MLCO2> than SC20, SC22 has a higher <MLCO2> than SC21, and 

SC23 has a higher <MLCO2> than SC22. Clearly, the expected value of <MLCO2> for SC24 is 

higher than that measured for SC23.

Figures 13a–e display scatter plots (for lag=0–5 yr) of <GLOTI> versus <AMO>, <SOI>, 

<NAO>, <PDO>, and <MLCO2>, respectively. For <GLOTI> versus <AMO>, two inferred 

regressions are drawn, one for SC12–SC19 and the other for SC20–SC23. For <GLOTI> versus 

<MLCO2>, only the inferred regression for SC20–SC23 is drawn. The statistics for the inferred 

regressions are given in table 4.
27

<GLOTI> (5)

0.6

–0.6

0

22

17

20 16

15

13 12

14

18

19

21

y12–23

(r = 0.92)

y12–21

(r = 0.70)

<AMO>

–0.3 0 0.3

<AMO>

–0.3 0 0.3

–0.3 0 0.3 –0.3 0 0.3

–0.3 0 0.3 –0.3 0 0.3

<GLOTI> (4)

0.6

–0.6

0

22 23

17

20 16

15

13 12

14

18

19

21

y20–23

(r = 0.91)

y12–19

(r = 0.75)

<GLOTI> (3)

0.6

–0.6

0

22 23

17

20

16

15

13 12

14

18

19

21

y20–23

(r = 0.91)

y12–19

(r = 0.80)

<GLOTI> (2)

0.6

–0.6

0

22 23

17

20

16

15

13 12

14

18

19

21

y20–23

(r = 0.91)

y12–19

(r = 0.81)

<GLOTI> (1)

0.6

–0.6

0

22 23

17

20

16

15

13 12

14

18

19

21

y20–23

(r = 0.93)

y13–19

(r = 0.89)

<GLOTI> (0)

0.6

–0.6

0

22

23

17

20 16

15

13

14

18

19

21

y20–23

(r = 0.94)

y13–19

(r = 0.91)

Figure 13a. Scatter plots of <GLOTI> versus <AMO> for lag 0–5 yr.
28

<GLOTI> (0)

0.6

–0.6

0

22

23

20 17

15

16

13

14

18

19

21

<GLOTI> (1)

0.6

–0.6

0

22

23

20 17

15

16

13

14

18

19

21

<GLOTI> (2)

0.6

–0.6

0

22

23

17 20

15

16

13

12

14

18

19

21

<GLOTI> (3) <GLOTI> (5)

0.6

–0.6

0

22

23

17 20

15

16

13

12

14

18 19

21

<GLOTI> (4)

0.6

–0.6

0

22

23

17 20

15

16

13

12

14

18 19

21

0.6

–0.6

0

22

23

20 17

15

16

13

12

14

18

19

21

<SOI>

–6 0 6

<SOI>

–6 0 6

–6 0 6 –6 0 6

–6 0 6 –6 0 6

Figure 13b. Scatter plots of <GLOTI> versus <SOI> for lag 0–5 yr.
29

<GLOTI> (3)

0.6

–0.6

0

22

23

17

20

16

15

13

12

14

18

19

21

<GLOTI> (4)

0.6

–0.6

0

22 23

17

20

16

15

13

12

14

18

19

21

<NAO>

–0.3 0 0.3

<NAO>

–0.3 0 0.3

–0.3 0 0.3 –0.3 0 0.3

–0.3 0 0.3 –0.3 0 0.3 <GLOTI> (5)

0.6

–0.6

0

22

23

17 20

16

15

13

12

14

18

19

21

<GLOTI> (2)

0.6

–0.6

0

22

23

17

20

16

15

13

14

12

18

19

21

<GLOTI> (1)

0.6

–0.6

0

22

23

17

20

16

15

13

14

18

19

21

<GLOTI> (0)

0.6

–0.6

0

22

23

17

20

16

15 13

14

18

19

21

Figure 13c. Scatter plots of <GLOTI> versus <NAO> for lag 0–5 yr.
30

<GLOTI> (1)

0.6

–0.6

0

22 23

17

20

16

15

14

18

19 21

<GLOTI> (2)

0.6

–0.6

0

22 23

17

20

16

15

14

18

19 21

<GLOTI> (3)

0.6

–0.6

0

22 23

17

20

16

15

14

18

19 21

<GLOTI> (4)

0.6

–0.6

0

22 23

17

20

16

15

14

18

19

21

<PDO>

–0.8 0 0.8

<PDO>

–0.8 0 0.8

–0.8 0 0.8 –0.8 0 0.8

–0.8 0 0.8 –0.8 0 0.8 <GLOTI> (5)

0.6

–0.6

0

22 23

17

20

16

15

14

18

19

21

<GLOTI> (0)

0.6

–0.6

0

22

23

17

20

16

15

14

18

19 21

Figure 13d. Scatter plots of <GLOTI> versus <PDO> for lag 0–5 yr.
31

<MLCO2>

300 400

<GLOTI> (5)

0.6

–0.6

0

22

23

20

21

y20–23

(r = 0.9987)

y20–23 (r = 0.9987)

<MLCO2>

300 400

300 400 300 400

300 400 300 400

 <GLOTI> (4)

0.6

–0.6

0

22

23

20

21

y20–23

(r = 0.9987)

y20–23 (r = 0.9987)

 <GLOTI> (3)

0.6

–0.6

0

22 23

20

21

y20–23

(r = 0.9987)

 <GLOTI> (2)

0.6

–0.6

0

22

23

20

21

y20–23

(r = 0.9994)

 <GLOTI> (1)

0.6

–0.6

0

22

23

20

21

y20–23

(r = 0.9992)

 <GLOTI> (0)

0.6

–0.6

0

22

23

20

21

y20–23

(r = 0.9989)

Figure 13e. Scatter plots of <GLOTI> versus <MLCO2> for lag 0–5 yr.
32Table 4. Correlations of SC-length averages of GLOTI against SC averages of selected climate parameters.

Lag 0, SC13–SC19 Lag 0, SC20–SC23 (n= 4)

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t cl

<AMO> –0.161 0.925 0.910 0.828 0.066 4.895 7 >99.5% <MLCO2> –3.756299 0.011460 0.9989 0.9978 0.015 27.666 >99.8%

<AMO> 0.326654 1.368739 0.9401 0.8838 0.098 3.900 >90%

Lag 1, SC13–SC19 Lag 1, SC20–SC23 (n= 4)

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t cl

<AMO> –0.160 0.925 0.890 0.793 0.074 4.362 7 >99% <MLCO2> –3.753224 0.011498 0.9992 0.9984 0.012 34.075 >99.9%

<AMO> 0.342169 1.358281 0.9301 0.8652 0.106 3.582 >90%

Lag 2, SC12–SC19 Lag 2, SC20–SC23 (n= 4)

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t cl

<AMO> –0.176 0.827 0.810 0.657 0.088 3.389 8 >99% <MLCO2> –3.683248 0.011342 0.9994 0.9988 0.012 34.964 >99.9%

<AMO> 0.356746 1.341576 0.9315 0.8677 0.104 3.6221 >90%

Lag 3, SC12–SC19 Lag 3, SC20–SC23 (n= 4)

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t cl

<AMO> –0.174 0.815 0.796 0.633 0.091 3.220 8 >98% <MLCO2> –3.621020 0.011211 0.9987 0.9975 0.017 23.335 >99.8%

<AMO> 0.370436 1.298026 0.9112 0.8303 0.116 3.128 >90%

Lag 4, SC12–SC19 Lag 4, SC20–SC23 (n= 4)

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t cl

<AMO> –0.173 0.747 0.748 0.559 0.098 2.757 8 >95% <MLCO2> –3.628428 0.011270 0.9987 0.9975 0.015 26.391 >99.8%

<AMO> 0.383674 1.301415 0.9088 0.8259 0.118 3.080 >90%

Lag 5, SC12–SC19 Lag 5, SC20–SC23 (n= 4)

Parameter a b r r 2 se t n cl Parameter a b r r 2 se t cl

<AMO> –0.170 0.711 0.702 0.493 0.106 2.426 8 >90% <MLCO2> –3.530094 0.011028 0.9987 0.9974 0.012 33.618 >99.9%

<AMO> 0.396926 1.290762 0.9211 0.8485 0.108 3.347 >90%
33

For the interval SC20–SC23, clearly, the strongest inferred regressions are those between 

<GLOTI> and <MLCO2>, having cl>99.8% and >99.9%, and se=0.01 °C. This suggests that 

one might be able to better estimate <GLOTI> for the current ongoing SC24, and perhaps future 

SC25 and beyond (presuming the validity of the fit), on the basis of having accurate estimates of 

<MLCO2> for these cycles.

From figure 12 (and table 3), it is clear that <MLCO2> is increasing over time. A simple linear fit of <MLCO2> versus SC yields y=7.344+15.839x, where y refers to <MLCO2> and x refers 

to the SC. The inferred regression has r=0.99807, r2=0.99615, se=1.557, t=22.74, and cl>99.8%. 

Presuming the validity of the fit, one estimates the <MLCO2> for SC24 and SC25, respectively, to 

be 387.48±1.56 ppm and 403.32±1.56 ppm (±1 se prediction interval). Applying these values in the 

inferred linear regressions (dependent upon selection of lag) results in <GLOTI>=0.68±0.02 °C for 

SC24 (lag=0 yr) to 0.74±0.01 °C (lag=5 yr) and <GLOTI>=0.87±0.02 °C for SC25 (lag=0 yr) to 

0.92±0.01 °C (lag=5 yr). Hence, the projected <GLOTI> for SC24 appears very likely to be higher 

than that measured for SC23; namely, <GLOTI>>0.526 °C (lag=0 yr) for SC24. If true, then this 

finding contradicts the prediction of Solheim et al.,96,97 who suggest that the <GLOTI> will be 

much cooler for SC24 as compared to SC23, a prediction based on the ongoing declining solar activity and the long duration of SC23.

Figure 14 compares annual values of the GLOTI for SC23 and SC24 for similar phasing 

(i.e., the elapsed time in years t from Emin). Plainly, the GLOTI measured during SC24 (2008–2012) 

has been higher every year than was seen for similar phasing in SC23, suggesting that, indeed, the 

<GLOTI> for SC24 will be higher than was measured for SC23 (0.526 °C).

1

0.5

0

0 2 4 6 8 10

0.526 °C

SC23

SC24

t, Elapsed Time in Years From Emin

GLOTI (°C)

Figure 14. Annual variation of GLOTI for SC23 (filled circles) and SC24 (filled triangles) 

for similar phasing.
34
35

3. DISCUSSION AND SUMMARY

This TP has examined SC-length averages of the January–December values of the GLOTI in 

relation to SC-length averages of various annual values of descriptors of solar-geomagnetic activity 

and climate, incorporating lags of 0–5 yr. For the interval SC12–SC21, the best inferred linear correlation is the one found between <GLOTI> and <aa(I:SSN)>, incorporating lag=5 yr and having 

r=0.969 and se=0.048 °C. The descriptor <aa(I:SSN)> is a proxy for the strength of the recurrent, 

long-lived events, like coronal holes, which tend to be more prevalent during the decline of the SC 

between cycle maximum amplitude and next SC minimum amplitude. For the interval SC20–SC23, 

the best inferred linear correlation is the one found between <GLOTI> and <MLCO2>, incorporating lag=2 yr and having r=0.9994 and se=0.012 °C. A comparison of <GLOTI> and <SSN> for 

SC12–SC21 shows that its best correlation is for lag=0 yr, having r=0.831 and se=0.093 °C, a result 

that contrasts that found by Stauning, who reports the best correlation to be the one incorporating 

lag=3 yr.62 Since the global temperature values (i.e., the GLOTI) are found to change slightly from 

year to year, it might be that this slight variation in their determination and the use of a slightly 

longer database (2–3 yr longer) used in the present study can account for the difference in the fits 

(i.e., best fit being lag=0 yr versus lag=3 yr). For the overall interval SC12–SC23, the correlation between <GLOTI> and <SSN> weakens considerably, having r<0.57 and se>0.23 °C for all 

lags 0–5 yr. Hence, SC22 (1986–1995) and SC23 (1996–2007) appear to be statistical outliers with 

respect to the inferred preferential linear relationship found between <GLOTI> and SC-length averages of solar-geomagnetic activity descriptors based on SC12–SC21. Recall that both GLOTI and 

<GLOTI> continue to rise (through SC23), while solar activity appears to be waning, suggesting 

that something other than solar-geomagnetic activity must now be responsible for the continued rise 

of global temperatures, especially since SC20.

Based on the inferred preferential linear correlation found between <MLCO2> and SC for 

SC20–SC23, having r=0.998 and se=1.56 ppm, one estimates <MLCO2> for SC24 to be about 

387.48±1.56 (the ±1 se prediction interval). Using this estimate (and lag=2 yr) for <MLCO2>, 

one further predicts <GLOTI>=0.71±0.02 °C for SC24, a value considerably larger than that seen 

for SC23 (0.551 °C for lag 2 yr). Hence, based on this analysis and assuming the validity of the 

inferred preferential linear correlation, one expects <GLOTI> to continue to rise in SC24 and to be 

warmer than was seen in SC23, a result in contrast to that given by Solheim et al.,96,97 who suggest 

that <GLOTI> will instead be much cooler for SC24 as compared to SC23, a prediction based on 

the declining levels of solar activity and long duration of SC23. (Based on extrapolated levels of 

<MLCO2>, one expects <GLOTI> to exceed 1 °C in SC26, its expected onset about 2030–2032.)

Now, while solar irradiance has been found to vary with solar activity98–105 (i.e., over the 

SC), it cannot account for the observed continued warming evident in <GLOTI>, especially since 

SC20. Nor can climate factors, such as the AMO, SOI, NAO, or PDO, account for the continuing 

increase in <GLOTI> that is currently being experienced. Instead, it appears that increased levels of 

greenhouse gases106–109 must be the underlying cause for the continued warming that has occurred, 

especially over the past 50 years or so (i.e., since onset for SC20). 
36

Figure 15 compares (a) GLOTI, (b) aa(SSN) and aa(I:SSN), (c) the annual greenhouse gases 

index (AGGI), and (d) the global radiative forcing of CO2, methane (CH4), nitrous oxide (NO2), 

and total greenhouse gases for the interval 1979–2012 (available online at <http://www.esrl.noaa.

gov/gmd/aggi/aggi.html>). Plainly, while the GLOTI is rising (in particular since 1985, with yearto-year variations of ±0.21 °C or less) during the interval 1979–2012, the overall cyclic variation 

of solar-geomagnetic activity (i.e., aa(SSN) and aa(I:SSN)) is now declining, and greenhouse gas 

radiative forcing is continuously rising. The decreasing solar-geomagnetic activity suggests that the 

Sun’s total irradiance must also be declining, while the increase in greenhouse gases suggests that 

more heat is being trapped than is being reradiated back into space. In particular, the GLOTI is 

found to correlate strongly with the AGGI, the total radiative forcing of greenhouse gases and the 

radiative forcing of CO2 (the chief contributor to the radiative forcing of greenhouse gases: >64% 

in 2012). For GLOTI versus AGGI, the inferred regression is y=–0.691+1.014x, having r=0.875, 

r2=0.765, se=0.09, t=10.096, and cl>99.9%. For GLOTI versus the total radiative forcing of 

greenhouse gases, the inferred regression is y=–0.691+0.466x, having r=0.874, r2=0.765, se=0.09, 

t=10.405, and cl>99.9%. For GLOTI versus the radiative forcing of CO2, the inferred regression is 

y=–0.535+0.653x, having r=0.878, r2=0.771, se=0.09, t=10.597, and cl>99.9%.

In conclusion, the inferred preferential linear relationship between <GLOTI> and SC-length 

averages of solar-geomagnetic activity that was apparent prior to SC21 (onset 1986) no longer 

appears to be the dominate factor once it was in the ongoing warming expressed by <GLOTI>. 

Instead, it is the increase in greenhouse gases (primarily CO2) that better correlates with the increase 

in <GLOTI>, in particular since SC20.
37

0.5

0

1

1.5

2

2.5

3

1980 1985 1990 1995 2000 2005 2010 2015

Year

(d)Wm–2

5

0

10

15

20

25

aa(SSN)

aa(I:SSN)

Total (Including CFC12, CFC11, and

 15 Minor Contributors)

CO2

CH4

NO2

(b)nT

0

0.5

1

(a)GLOTI

1

0.5

1.5

(c)AGGI

Figure 15. Annual variation of (a) GLOTI, (b) aa(SSN) and aa(I:SSN), (c) the AGGI,

and (d) the radiative forcing of NO2, CH4, CO2, and total (including CFC12,

CFC11, and 15 minor contributors) for the interval 1979–2012.
38

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On the Relationship Between Global Land-Ocean Temperature 

and Various Descriptors of Solar-Geomagnetic Activity and Climate

Robert M. Wilson

George C. Marshall Space Flight Center

Huntsville, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 47

Availability: NASA STI Information Desk (757–864–9658)

Prepared by the Science and Research Office, Science and Technology Office

M–1382

Technical Publication

NASA/TP—2014–218193

Global Land-Ocean Temperature Index, climatic change, climate, sunspot cycle

01–04–2014

UU 62

NASA

U U U

Examined are sunspot cycle- (SC-) length averages of the annual January–December values of the Global Land-Ocean Temperature Index (<GLOTI>) in 

relation to SC-length averages of annual values of various descriptors of solar-geomagnetic activity and climate, incorporating lags of 0–5 yr. For the 

overall interval SC12–SC23, the <GLOTI> is inferred to correlate best against the parameter <aa(I:SSN)> incorporating lag=5 yr, where the parameter 

<aa(I:SSN)> refers to the resultant aa value having removed that portion of the annual aa average value due to the yearly variation of sunspot number 

(SSN). The inferred correlation between the <GLOTI> and <aa(I:SSN)> is statistically important at confidence level cl>99.9%, having a coefficient of 

linear correlation r=0.865 and standard error of estimate se=0.149 °C. Excluding the most recent cycles SC22 and SC23, the inferred correlation is stronger, 

having r=0.969 and se=0.048 °C. With respect to the overall trend in the <GLOTI>, which has been upwards towards warmer temperatures since SC12 

(1878–1888), solar-geomagnetic activity parameters are now trending downwards (since SC19). For SC20–SC23, in contrast, comparison of the <GLOTI> 

against SC-length averages of the annual value of the Mauna Loa carbon dioxide (<MLCO2>) index is found to be highly statistically important (cl»99.9%), 

having r=0.9994 and se=0.012 °C for lag=2 yr. On the basis of the inferred preferential linear correlation between the <GLOTI> and <MLCO2>, 

the current ongoing SC24 is inferred to have <GLOTI> warmer than was seen in SC23 (i.e., >0.526 °C), probably in excess of 0.68 °C (relative to the 

1951–1980 base period).

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